Problem: Simplify the expression. $ (q^{6}-q^{5}+7q) - ( -7q^{6}-5q^{3}+5q) $
Distribute any negative signs. $(q^{6}-q^{5}+7q) + (7q^{6}+5q^{3}-5q)$ Since we are adding polynomials, we can simply remove the parentheses. $q^{6}-q^{5}+7q + 7q^{6}+5q^{3}-5q$ Identify like terms. $ { q^6} - \color{#DF0030}{ q^5} + \color{#9D38BD}{7 q} + {7 q^6} + {5 q^3} - \color{#9D38BD}{5 q} $ Combine like terms. $ { ( 1 + 7 ) q^6} + \color{#DF0030}{ -1 q^5} + { 5 q^3} + \color{#9D38BD}{ q} $ Add the coefficients. $8q^{6}-q^{5}+5q^{3}+2q$